Question

A particular isotope has a​ half-life of 55 days. If you start with 1 kilogram of this​ isotope, how much will remain after 120 ​days? after 240 ​days? ​(Round to three decimal places as​ needed.)

Answer 1

Given the half-life, you have enough information to find the decay factor
`k` that satisfies


`\frac12=e^(55k)\implies k=-(\ln2)/(55)\approx-0.013`

Starting with 1 kg of the isotope, after 120 days you would be left with


`y=e^(120k)=\frac1{2^(24/11)}\approx0.220\text{ kg}`

After 240 days, you would have


`y=e^(240k)=\frac1{2^(48/11)}\approx0.049\text{ kg}`